The mitotic spindle forms during cell division and separates chromosomes into the daughter cells. It is required for normal eukaryotic cell division. In most cells, the division plane position and orientation is controlled by spindle position and orientation. However, the force mechanisms underlying spindle positioning are ill-understood. Two alternative models have been proposed. One invokes microtubule interactions with the cell cortex, and the other with the cell cytoplasm. The goal is to discover which model (if not both) is correct by using modeling, simulation, and experiments in C. elegans early embryos. The project team has skills in biophysical theory, experiment, mathematical modeling, and simulation. An essential difference between the two models is whether microtubules interact actively or passively with the cytoplasm, but given the system's complexity it is difficult to discriminate with experiment alone. We will use modeling and simulation to predict cytoplasmic flows associated with each model, and their combinations, and compare these to experimental measurements of actual flows. Detailed hydrodynamic interactions have not been previously accounted for in modeling spindle dynamics, and requires novel methods for efficiently and accurately capturing spindle microtubules interacting with each other, the cytoplasmic fluid, and the cell periphery. We will compare the predicted dynamics to new experimental measurements that simultaneously capture spindle structure and dynamics, and cytoplasmic motions. Comparisons will be made between predicted and observed responses under physical, molecular, and genetic perturbations. Intellectual Merit: The proposed work will bring a new approach to modeling mitotic spindle dynamics and positioning. The integrated experimental and theoretical approach will enable new insights into the mechanisms of positioning and asymmetric cell division. The project will contribute to the broader efforts to understand the mitotic spindle and cell division, a long-standing fundamental problem in cell biology. This work will expand technical knowledge in cellular biology, biophysics, experimental technique, statistical physics, applied math, fluid dynamics, partial differential equations, and numerical analysis.